Adaptive structures involving large imposed deformation often go beyond the boundary of linear theory and they should be treated as “nonlinear” structures. A generic nonlinear finite element formulation for vibration sensing and control analysis of laminated electro/elastic nonlinear shell structures is derived based on the virtual work principle. A generic curved triangular piezoelectric shell element is proposed based on the layerwise constant shear angle theory. The dynamic system equations, equations of electric potential output and feedback control force defined in a matrix form are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. A finite element code for vibration sensing and control analysis of nonlinear active piezoelectric structronic systems is developed. The developed piezoelectric shell element and finite element code are validated and then applied to control analysis of flexible electro-elastic (piezoelectric/elastic) structural systems. Vibration control of constant-curvature electro/elastic beam and plate systems are studied. Time-history responses of free and controlled nonlinear electro/elastic beam and plate systems are presented and nonlinear effects discussed.

Effective control of toroidal shells, e.g., cooling tubes, space colonies, inflatable space structures, etc., enhances their operational precision, accuracy, and reliability. Dynamics and control effectiveness of toroidal shell panels laminated with distributed piezoelectric sensor/actuator layers are investigated in this study. Mathematical model and finite element formulations of piezo(electric)-elastic shell structures are presented. Element and system matrix equations of the piezoelastic shell structronic (sensor/actuator/structure/control) system are defined and the system equations reveal the coupling of mechanical and electric (or control) fields. Free vibration analyses of two toroidal shells are investigated and compared favorably with published data. Two sensor/actuator configurations based on identical sensor/actuator sizes, namely the parallel configuration and the diagonal configuration, laminated on the toroidal shell are investigated and analysis data suggest that the diagonal configuration provides better control effects, as compared with the parallel configuration. The parallel configuration is ineffective to anti-symmetrical modes; the diagonal configuration is effective to most natural modes and ineffective to quad-anti-symmetrical modes with respect to the panel center.

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Conical shells and components are widely used as nozzles, injectors, rocket fairings, turbine blades, etc. Dynamic and vibration characteristics of conical shells have been investigated over the years. In this paper, electromechanics and distributed sensing phenomena of a generic double-curvature shell and a conical shell are discussed, and governing sensing signal-displacement equations are derived. Spatially distributed modal voltages and signal generations of conical shells laminated with distributed piezoelectric sensor layers or neurons are investigated based on the Donnel-Mushtari-Valsov theory. Distributed modal voltages and their various signal components of conical shell models reveal that the dominating signal component among the four contributing signal components is the circumferential membrane component. This dominance is even more significant for lower shell modes and/or deep shells. In general, high strain regions result in high signal magnitudes. Accordingly, the spatially distributed signal patterns — the modal voltages — clearly represent the modal dynamic and strain characteristics of conical shells.

Adaptive structures involving large imposed deformation often go beyond the boundary of linear theory and they should be treated as “nonlinear” structures. A generalized nonlinear finite element formulation for vibration sensing and control analysis of laminated electro/elastic nonlinear shell structures is derived based on the virtual work principle. A generic curved triangular piezoelectric shell element is proposed based on the layerwise constant shear angle theory. The dynamic system equations, equations of electric potential output and feedback control force defined in a matrix form are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. The developed piezoelectric shell element and finite element code are validated and then applied to control analysis of flexible electro-elastic (piezoelectric/elastic) structural systems. Vibration control of constant-curvature electro/elastic beam and plate systems is studied. Time-history responses of free and controlled nonlinear electro/elastic beam and plate systems are presented and nonlinear effects discussed.